Sweep along a path through multiple cross-sections
i'll further update the answer if you upload a demo blend with those shapes. I'd like to give you a nice answer.

For now, i'll clarify what i've said in the comment, with an illustration. For predictable results I recommend making sure all profiles have the same vertex count. There are two ways to do that.

subdivide the square profile.



or, double up on the destination vertices.



notice that the locations of the vertices in this "doubled up" example will produce some undesirable twisting in the end result. 



One simple way is to interpolate both UV (slices between profiles) - without a path or trajectory". Notice how the extrusion goes exactly through the profiles too.



In the above example you must position and rotate the profiles in such a way as to achieve minimal stretching. Sverchok's Object In node interprets each Curve as a list of Vertices (the vertex indices are sequential and stable from Curve objects) and we interpolate between the list of resulting profiles. Get the .blend on this issue